The next step is digging a little deeper into his online activity. Checking his browser history is basic but if he’s at all savvy, he’ll be doing his dirty business in stealth mode. Next, if you can, check his phone for hidden apps or folders. There’s a little iPhone trick for hiding folders or security apps like NQ Mobile Vault. Even if you can’t see what the hidden files are, the fact that they’re hidden is a warning sign.
If you want to take things to the next level, you can install spyware, like FlexiSpy, on your partner’s phone to monitor messages, calls and other activity. Bear in mind, that’s a serious breach of his privacy and you might not like what you hear, so think long and hard before going that route.